怎么计算这题的不定积分(高数)
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 12:53:36
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怎么计算这题的不定积分(高数)
怎么计算这题的不定积分(高数)
怎么计算这题的不定积分(高数)
1/[x^2 (1+x^2)] = 1/x^2 - 1/(1+x^2)
∫dx/[x (1+x^2)] =
∫xdx/[x^2 (1+x^2)]=
=(1/2)∫ [ 1/x^2 - 1/(1+x^2) ]d(x^2)
=(1/2)ln x^2 -(1/2) ln(1+x^2) + C
=(1/2) ln [x^2 /(1+x^2)] +C